?7 / (4 + ?2) = [7 / (4 + ?2)] x [(4 - ?2 ) / (4 - ?2]
= 7(4 - ?2) / (16 - 2)
[? (a + b)(a - b) = a² - b²]
= 7(4 - ?2 )/14
= (4 - ?2)/2
= (4 - 1.4142)/2
= 2.5858/2 = 1.2929

(0.96)³ - (0.1)³/ [(0.96)³ + 0.096 + 0.01]
= (0.96)³ - (0.1)³ = (0.96 - 0.1) [(0.96)² + 0.96 x 0.1 + (0.1)²]
[? a³ - b³ = (a - b) (a² + ab + b²)]
= (0.96 - 0.1) [(0.96)² + 0.096 + 0.01]/(0.96)² + 0.096 + 0.01
= 0.96 - 0.1 = 0.86

? = 3²/₃ + 2³/₄ + 1¹/₂
= 3 + 2 + 1 + (2/3 + 3/4 + 1/2)
= 6 + (8 + 9 + 6)/12 = 6 + (23/12)
= 6 + (1¹¹/₁₂) = 7¹¹/₁₂

(?)^1/2 = (5568 ÷ 87)^1/3 + (72 x 2)^1/2
= (64)^1/3 + (144)^1/2
? ? = (4 + 12)² = 256

(70 ÷ 100) ^{? + 3} = (0.49)⁴ x (0.343)⁴ ÷ (0.2401)⁴
(0.7) ^{? + 3} = (0.49 x 0.343/0.2401)⁴
(0.7)^{? + 3} = (0.7)⁴
On comparing the exponents both sides, we get
? + 3 = 4
? ? = 4 - 3 = 1

Given expression
= a³+ b³ + c³ - 3abc/a² + b² + c² - ab - bc - ca
= a + b + c
= 0.5 + 0.2 + 0.3
where, a = 0.5, b = 0.2, c = 0.3

[725 x 725 x 725 + 371 x 371 x 371] / [725 x 725 - 725 x 371 + 371 x 371]
= 725 + 371 = 1096
[? (a³ + b³) / (a² - ab + b²) = (a + b) (a² - ab + b²)/(a² - ab + b²) = a + b ]

We know that, (a + b)² = a² + b² + 2ab
= 234 + 2 x 108 = 450
(a - b)² = a² + b² - 2ab
= 234 - 2 x 108 = 18
? (a + b)²/(a - b)² = 450/18 = 25
? [(a + b)/(a - b)]² = 25
? (a + b)/(a - b) = ?25 = 5

Given expression = 2x² + 2/3x² + 3 + 5x
On dividing numerator and denominator by x, we get
= 2(x + 1/x)/3(x + 1/x) + 5 = 2 x 2/3 x 2 + 5 = 4/11
[given x + 1/x = 2]

? a + (1/b) = 1
ab + 1 = b ......(i)

Also, b + (1/c) = 1
? b = 1 - (1/c) ....(ii)

From Eqs. (i) and (ii), we get
ab + 1 = 1 - (1/c)
? ab = -1/c
? abc = -1